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<table width="100%" summary="page for cake"><tr><td>cake</td><td style="text-align: right;">R Documentation</td></tr></table>

<h2>Breakage Angle of Chocolate Cakes</h2>

<h3>Description</h3>

<p>Data on the breakage angle of chocolate cakes made with
three different recipes and baked at six different
temperatures.  This is a split-plot design with the
recipes being whole-units and the different temperatures
being applied to sub-units (within replicates). The
experimental notes suggest that the replicate numbering
represents temporal ordering.
</p>


<h3>Format</h3>

<p>A data frame with 270 observations on the following 5 variables.
</p>

<dl>
<dt><code>replicate</code></dt><dd><p>a factor with levels <code>1</code> to <code>15</code></p>
</dd>
<dt><code>recipe</code></dt><dd><p>a factor with levels <code>A</code>, <code>B</code> and <code>C</code></p>
</dd>
<dt><code>temperature</code></dt><dd><p>an ordered factor with levels <code>175</code>
&lt; <code>185</code> &lt; <code>195</code> &lt; <code>205</code> &lt; <code>215</code> &lt; <code>225</code></p>
</dd>
<dt><code>angle</code></dt><dd><p>a numeric vector giving the angle at which the
cake broke.</p>
</dd>
<dt><code>temp</code></dt><dd><p>numeric value of the baking temperature (degrees F).</p>
</dd>
</dl>


<h3>Details</h3>

<p>The <code>replicate</code> factor is nested within the
<code>recipe</code> factor, and <code>temperature</code> is nested
within <code>replicate</code>.
</p>


<h3>Source</h3>

<p>Original data were presented in Cook (1938), and reported
in Cochran and Cox (1957, p. 300).  Also cited in Lee,
Nelder and Pawitan (2006).
</p>


<h3>References</h3>

<p>Cook, F. E. (1938) <em>Chocolate cake, I. Optimum
baking temperature</em>. Master's Thesis, Iowa State College.
</p>
<p>Cochran, W. G., and Cox, G. M. (1957) <em>Experimental
designs</em>, 2nd Ed.  New York, John Wiley \&amp; Sons.
</p>
<p>Lee, Y., Nelder, J. A., and Pawitan, Y. (2006)
<em>Generalized linear models with random effects.
Unified analysis via H-likelihood</em>. Boca Raton, Chapman
and Hall/CRC.
</p>


<h3>Examples</h3>

<pre>
str(cake)
## 'temp' is continuous, 'temperature' an ordered factor with 6 levels

(fm1 &lt;- lmer(angle ~ recipe * temperature + (1|recipe:replicate), cake, REML= FALSE))
(fm2 &lt;- lmer(angle ~ recipe + temperature + (1|recipe:replicate), cake, REML= FALSE))
(fm3 &lt;- lmer(angle ~ recipe + temp        + (1|recipe:replicate), cake, REML= FALSE))

## and now "choose" :
anova(fm3, fm2, fm1)
</pre>


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